Determine the shear stress acting on plane ab and the

Question

Problem 1:

The stress acting on two planes at point, P, is shown in the figure below. Determine the shear stress, acting on plane AB and the principal stresses at the point.

Problem 2:

A pressure-shear test is conducted on a specimen of rock gouge. A normal pressure p and shear stress Τ are applied to the specimen as shown. The lateral stress components σ_z, - Τ_zx and Τ_zy, are negligible.

The test was run with p = 20 MPa and Τ = 60 MPa. A post-mortem examination of the specimen reveals slip bands 60. degrees to the horizontal direction. Assuming that slip occurs on the bands when

|Τ_n| = f|σ_n|

find the friction coefficient f.